Question

Find the distance from point A (-1/4,5)

to the line - x + 2y = 14. Round your answer to the nearest tenth.

Answer 1

1.7 (units).

Explanation:

1) if the point A has (-0.25;5) and the equation of the given line is -x+2y=14 (Ax+By+C=0), then the required distance can be calculated according to the formula:

`d=(Ax_0+By_0+C)/(√(A^2+B^2) )` , where A, B and C belong to the given line, x₀, y₀ - coordinates of the given point;

2) A=-1, B=2, C=-14 and x₀=-0.25, y₀=5, then according to the formula above:

`d=|(0.25+5*2-14)/(√(4+1))|=(3.75)/(√(5))=(3.75)/(2.2)=1.7`